Föllmer, Hans
Overview
Works:  70 works in 166 publications in 3 languages and 1,356 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  HG176.5, 332.01519232 
Publication Timeline
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Most widely held works by
Hans Föllmer
Stochastic finance : an introduction in discrete time by
Hans Föllmer(
Book
)
41 editions published between 2002 and 2016 in English and held by 613 WorldCat member libraries worldwide
This is the third, revised and extended edition of the classical introduction to the mathematics of finance, based on stochastic models in discrete time. In the first part of the book simple oneperiod models are studied, in the second part the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Due to the strong appeal and wide use of this book, it is now available as a textbook with exercises. It will be of value for a broad community of students and researchers. It may serve as basis for graduate courses and be also interesting for those who work in the financial industry and want to get an idea about the mathematical methods of risk assessment .Hans Föllmer, HumboldtUniversität zu Berlin, Germany; Alexander Schied, University of Mannheim, Germany
41 editions published between 2002 and 2016 in English and held by 613 WorldCat member libraries worldwide
This is the third, revised and extended edition of the classical introduction to the mathematics of finance, based on stochastic models in discrete time. In the first part of the book simple oneperiod models are studied, in the second part the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Due to the strong appeal and wide use of this book, it is now available as a textbook with exercises. It will be of value for a broad community of students and researchers. It may serve as basis for graduate courses and be also interesting for those who work in the financial industry and want to get an idea about the mathematical methods of risk assessment .Hans Föllmer, HumboldtUniversität zu Berlin, Germany; Alexander Schied, University of Mannheim, Germany
Stochastic processes and related topics(
Book
)
6 editions published in 1996 in English and held by 65 WorldCat member libraries worldwide
6 editions published in 1996 in English and held by 65 WorldCat member libraries worldwide
Chemistry and mathematics: two scientific languages of the 21st century : LeopoldinaSymposium [Göttingen, October 11 to
13, 2001] by Leopoldina Symposium(
Book
)
8 editions published in 2003 in English and held by 52 WorldCat member libraries worldwide
8 editions published in 2003 in English and held by 52 WorldCat member libraries worldwide
École d'Été de Probabilités de SaintFlour XVXVII, 198587(
)
1 edition published in 1988 in English and held by 29 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 29 WorldCat member libraries worldwide
Ecole d'été de probabilités de SaintFlour XVXVII, 198587 by
Ecole d'Eté de Probabilités(
Book
)
6 editions published in 1988 in 3 languages and held by 18 WorldCat member libraries worldwide
This volume contains detailed, workedout notes of six main courses given at the SaintFlour Summer Schools from 1985 to 1987
6 editions published in 1988 in 3 languages and held by 18 WorldCat member libraries worldwide
This volume contains detailed, workedout notes of six main courses given at the SaintFlour Summer Schools from 1985 to 1987
Berträge zur Theorie der stochastischen Prozesse by
Hans Föllmer(
Book
)
4 editions published in 1972 in German and held by 9 WorldCat member libraries worldwide
4 editions published in 1972 in German and held by 9 WorldCat member libraries worldwide
On Schrödinger processes in infinite dimensions by
Hans Föllmer(
Book
)
3 editions published in 1995 in English and held by 8 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 8 WorldCat member libraries worldwide
Convex measures of risk and trading constraints by
Hans Föllmer(
Book
)
3 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et aL (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust not ion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is closely related to the superhedging duality under convex constraints
3 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et aL (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust not ion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is closely related to the superhedging duality under convex constraints
On Itô's formula for multidimensional Brownian motion by
Hans Föllmer(
Book
)
3 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
Consider a ddimensional Brownian motion X (Xl, ... ,Xd ) and a function F which belongs locally to the Sobolev space W 1,2. We prove an extension of Ito's formula where the usual second order terms are replaced by the quadratic covariations [fk(X), Xkj involving the weak first partial derivatives fk of F. In particular we show that for any locally squareintegrable function f the quadratic covariations [f(X), Xkj exist as limits in probability for any starting point, except for some polar set. The proof is based on new approximation results for forward and backward stochastic integrals.  Ito's formula ; Brownian motion ; stochastic integrals ; quadratic covariation ; Dirichlet spaces ; polar sets
3 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
Consider a ddimensional Brownian motion X (Xl, ... ,Xd ) and a function F which belongs locally to the Sobolev space W 1,2. We prove an extension of Ito's formula where the usual second order terms are replaced by the quadratic covariations [fk(X), Xkj involving the weak first partial derivatives fk of F. In particular we show that for any locally squareintegrable function f the quadratic covariations [f(X), Xkj exist as limits in probability for any starting point, except for some polar set. The proof is based on new approximation results for forward and backward stochastic integrals.  Ito's formula ; Brownian motion ; stochastic integrals ; quadratic covariation ; Dirichlet spaces ; polar sets
Efficient hedging cost versus shortfall risk by
Hans Föllmer(
Book
)
3 editions published in 1999 in English and held by 7 WorldCat member libraries worldwide
An investor faced with a contingent claim may eliminate risk by (super)hedging in a financial market. As this is often quite expensive, we study partial hedges, which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal probability, given a capital constraint. Here we look for strategies which minimize the shortfall risk defined as the expectation of the shortfall weighted by some loss function. The resulting efficient hedges allow the investor to interpolate in a systematic way between the extremes of no hedge and a perfect (super)hedge, depending on the accepted level of shortfall risk.  risk management ; stochastic volatility ; shortfall risk ; Hedging ; efficient hedges ; lower partial moments ; convex duality
3 editions published in 1999 in English and held by 7 WorldCat member libraries worldwide
An investor faced with a contingent claim may eliminate risk by (super)hedging in a financial market. As this is often quite expensive, we study partial hedges, which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal probability, given a capital constraint. Here we look for strategies which minimize the shortfall risk defined as the expectation of the shortfall weighted by some loss function. The resulting efficient hedges allow the investor to interpolate in a systematic way between the extremes of no hedge and a perfect (super)hedge, depending on the accepted level of shortfall risk.  risk management ; stochastic volatility ; shortfall risk ; Hedging ; efficient hedges ; lower partial moments ; convex duality
Stock price fluctuation as a diffusion in a random environment by
Hans Föllmer(
Book
)
3 editions published in 1993 in English and German and held by 7 WorldCat member libraries worldwide
3 editions published in 1993 in English and German and held by 7 WorldCat member libraries worldwide
A microeconomic approach to diffusion models for stock prices by
Hans Föllmer(
Book
)
3 editions published in 1992 in English and German and held by 7 WorldCat member libraries worldwide
3 editions published in 1992 in English and German and held by 7 WorldCat member libraries worldwide
Canonical decomposition of linear transformations of two independent Brownian motions by
Hans Föllmer(
Book
)
3 editions published in 1998 in English and held by 6 WorldCat member libraries worldwide
Motivated by the KyleBack model of "insider trading", we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition as semimartingales in their own filtration. In particular we characterize those transformations which generate again a Brownian motion.  Brownian motion ; insider trading ; stochastic filtering theory ; enlargement of filtration ; canonical decomposition ; SturmLiouville equation ; Volterra kernels
3 editions published in 1998 in English and held by 6 WorldCat member libraries worldwide
Motivated by the KyleBack model of "insider trading", we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition as semimartingales in their own filtration. In particular we characterize those transformations which generate again a Brownian motion.  Brownian motion ; insider trading ; stochastic filtering theory ; enlargement of filtration ; canonical decomposition ; SturmLiouville equation ; Volterra kernels
Probabilistic aspects of financial risk by
Hans Föllmer(
Book
)
3 editions published in 2000 in English and held by 6 WorldCat member libraries worldwide
Problems arising in Finance have become a significant source of new developments in Stochastic Analysis. We discuss some recent case studies, in particular some decomposition and representation theorems which are motivated by problems of hedging derivatives and of intertemporal consumption choice
3 editions published in 2000 in English and held by 6 WorldCat member libraries worldwide
Problems arising in Finance have become a significant source of new developments in Stochastic Analysis. We discuss some recent case studies, in particular some decomposition and representation theorems which are motivated by problems of hedging derivatives and of intertemporal consumption choice
On weak Brownian motions of arbitrary order by
Hans Föllmer(
Book
)
3 editions published in 1999 in English and held by 6 WorldCat member libraries worldwide
We show the existence, for any k E N, of processes which have the same kmarginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law P' of such a "weak Brownian motion of order k" can be constructed to be equivalent to Wiener measure P' on c [O, 1]. On the other hand, there are weak Brownian motions of arbitrary order whose law is singular to Wiener measure. We also show that, for any e > 0, there are weak Brownian motions whose law coincides with wiener measure outside of any interval of length e.  Brownian motion ; weak Brownian motion ; weak martingale ; marginals ; Volterra kernel
3 editions published in 1999 in English and held by 6 WorldCat member libraries worldwide
We show the existence, for any k E N, of processes which have the same kmarginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law P' of such a "weak Brownian motion of order k" can be constructed to be equivalent to Wiener measure P' on c [O, 1]. On the other hand, there are weak Brownian motions of arbitrary order whose law is singular to Wiener measure. We also show that, for any e > 0, there are weak Brownian motions whose law coincides with wiener measure outside of any interval of length e.  Brownian motion ; weak Brownian motion ; weak martingale ; marginals ; Volterra kernel
Convergence of locally and globally interacting Markov chains by
Hans Föllmer(
Book
)
3 editions published in 2001 in English and held by 6 WorldCat member libraries worldwide
We study the long run behaviour of interactive Markov chains on infinite product spaces. In view of microstructure models of financial markets, the interaction has both a local and a global component. The convergence of such Markov chains is analyzed on the microscopic level and on the macroscopic level of empirical fields. We give sufficient conditions for convergence on the macroscopic level. Using a perturbation of the DobrushinVasserstein contraction technique we show that macroscopic convergence implies weak convergence of the underlying Markov chain. This extends the basic convergence theorem of Vasserstein (1969) for locally interacting Markov chains to the case where an additional global component appears in the interaction.  Markov chains on infinite product spaces ; convergence of Markov chains ; contraction techniques ; Gibbs measures
3 editions published in 2001 in English and held by 6 WorldCat member libraries worldwide
We study the long run behaviour of interactive Markov chains on infinite product spaces. In view of microstructure models of financial markets, the interaction has both a local and a global component. The convergence of such Markov chains is analyzed on the microscopic level and on the macroscopic level of empirical fields. We give sufficient conditions for convergence on the macroscopic level. Using a perturbation of the DobrushinVasserstein contraction technique we show that macroscopic convergence implies weak convergence of the underlying Markov chain. This extends the basic convergence theorem of Vasserstein (1969) for locally interacting Markov chains to the case where an additional global component appears in the interaction.  Markov chains on infinite product spaces ; convergence of Markov chains ; contraction techniques ; Gibbs measures
Probabilistic aspects of options by
Hans Föllmer(
Book
)
3 editions published in 1991 in German and English and held by 6 WorldCat member libraries worldwide
3 editions published in 1991 in German and English and held by 6 WorldCat member libraries worldwide
Quantile hedging by
Hans Föllmer(
Book
)
3 editions published in 1998 in English and held by 6 WorldCat member libraries worldwide
In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling to spend that much, and who is ready to use a hedging strategy which succeeds with high probability.  Hedging ; superhedging ; Neyman Pearson lemma ; stochastic volatility ; value at risk
3 editions published in 1998 in English and held by 6 WorldCat member libraries worldwide
In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling to spend that much, and who is ready to use a hedging strategy which succeeds with high probability.  Hedging ; superhedging ; Neyman Pearson lemma ; stochastic volatility ; value at risk
Hedging of nonredundant contingent claims by
Hans Föllmer(
Book
)
3 editions published between 1985 and 1987 in English and German and held by 4 WorldCat member libraries worldwide
3 editions published between 1985 and 1987 in English and German and held by 4 WorldCat member libraries worldwide
The financial crisis and the systemic failure of academic economics(
)
2 editions published in 2009 in English and held by 4 WorldCat member libraries worldwide
The economics profession appears to have been unaware of the long buildup to the current worldwide financial crisis and to have significantly underestimated its dimensions once it started to unfold. In our view, this lack of understanding is due to a misallocation of research efforts in economics. We trace the deeper roots of this failure to the profession's insistence on constructing models that, by design, disregard the key elements driving outcomes in realworld markets. The economics profession has failed in communicating the limitations, weaknesses, and even dangers of its preferred models to the public. This state of affairs makes clear the need for a major reorientation of focus in the research economists undertake, as well as for the establishment of an ethical code that would ask economists to understand and communicate the limitations and potential misuses of their models.  Financial crisis ; academic moral hazard ; ethic responsibility of researchers
2 editions published in 2009 in English and held by 4 WorldCat member libraries worldwide
The economics profession appears to have been unaware of the long buildup to the current worldwide financial crisis and to have significantly underestimated its dimensions once it started to unfold. In our view, this lack of understanding is due to a misallocation of research efforts in economics. We trace the deeper roots of this failure to the profession's insistence on constructing models that, by design, disregard the key elements driving outcomes in realworld markets. The economics profession has failed in communicating the limitations, weaknesses, and even dangers of its preferred models to the public. This state of affairs makes clear the need for a major reorientation of focus in the research economists undertake, as well as for the establishment of an ethical code that would ask economists to understand and communicate the limitations and potential misuses of their models.  Financial crisis ; academic moral hazard ; ethic responsibility of researchers
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Related Identities
 Schied, Alexander
 Zabczyk, Jerzy Editor
 Engelbert, Hans Jürgen Editor
 Diaconis, Persi (1945....). Author
 Elworthy, Kenneth David (1940....).
 Hennequin, PaulLouis Editor
 Nelson, Edward (1932....).
 Papanicolaou, George (1943....).
 Varadhan, Srinivasa R. S.
 Sonderforschungsbereich Quantifikation und Simulation Ökonomischer Prozesse
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Alternative Names
Föllmer, H.
Föllmer, H. 1941
Föllmer, H. (Hans)
Föllmer, Hanns 1941
Follmer, Hans
Hans Föllmer deutscher Statistiker und Finanzmathematiker
Hans Föllmer Duits wiskundige
Hans Föllmer German mathematician
Hans Föllmer tysk matematikar
Hans Föllmer tysk matematiker
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